Quantum Mechanical Insights into Biological Processes at the Electronic Level - Computational Modeling of Biological Systems - page 127

Fig. 1 Scan along the R.H-H/ coordinate for the H2 molecule performed at the HF/6-31G and
CASSCF(2,2)/6-31G levels of theory. It is obvious that HF is unable to properly treat the singlet
diradical that forms at large H-H separations, and creates an excited state, H C C H . On the other

hand, CASSCF dissociates the molecule properly on two neutral H atoms

with singlet diradicals. As a result, HF will dissociate the H 2 molecule into H and
H C , which is an excited state for the system at large distances (Fig. 1 ). The reason
is that at large distances, the system again needs to be represented by two Slater
determinants, and not just one.
The methods that fit the bill are called multireference methods. They allow many
Slater determinants to contribute to the total wave function. The simplest such
method is configuration interaction (CI) [ 5 , 6 ]. The total CI wave function is literally
a normalized linear combination of the ground and excited state Slater determinants
in which the expansion coefficients c i are variationally optimized:

n

X

c i .i/ : ‰ D (26)

i D 1

CIS includes only the ground and singly excited determinants, CISD also
includes doubly excited determinants, and full CI includes all possible excitations,
as far as the basis set permits. Notice that the ground state MOs expanded in terms of
basis set functions remain fixed in CI, and only the coefficients in front of the Slater
determinants are optimized. This is an approximation, because in reality, excited
state MOs may be slightly different. CI is a simple method that is acceptable in
treatment of open-shell low spin systems.